Biased numbers and independent numbers are NOT mutually excusive ? What is your justification for that statement ?
If you find that a wheel is biased you bet on the biased numbers, that's it. There's no waiting for triggers, no hit and run, you just bet on the biased numbers for as long as the bias exists (I'm talking about genuine bias not just normal variance). There is no trigger involved unless you count identifying the bias as a "trigger", but it's not a trigger in the usual sense that a system player uses the term.
If outcomes are dependent it means that there is some regular pattern or sequence which "triggers" another pattern or sequence. If outcomes are independent there is no pattern which triggers or influences other patterns, which is why triggers don't work in roulette, although many system players believe they do, so you see them starting to bet when some numbers are hot because they think that this will somehow make them stay hot.
Why should outcomes be dependent? The only example I can think of would be if the casino was cheating you. Say for example you were using a positive martingale on red. After a few wins the casino might turn on magnets which deflected the ball away from red, so the trigger would be to start betting black after a few reds in a row. This would work if you knew what the casino was doing.
But this is a pretty far-fetched scenario and we can assume that 99.999% of the time the outcomes are independent. But some numbers could be biased. Biased doesn't mean dependent. Even though some numbers have a greater chance of hitting than other numbers it doesn't mean that just because the numbers haven't hit in a while it means they are "due"; that's still gambler's fallacy.